In [21]:
# Ultilizamos la libreria de seaborn para mostrar de forma más visual los factores de paso
Incurred_tr.heatmap_linkf()
En este documento, vamos a tratar de hacer uso de Python para tratar, analizar y calcular reservas de No Vida mediante la aplicación de métodos actuariales en Python.
Ya existen paquetes para facilitar esta labor, como el paquete chainladder. Este paquete o modulo es una herramienta muy completa, que incorpora gran cantidad de métodos integrados en sus funciones. Sin embargo, en este documento no vamos a abarcar el uso de esta herramienta (tal vez en el futuro hagamos un recorrido por las funciones que integra).
La finalidad de este documento es acercar el uso de Python al cálculo de reservas en el ámbito de los seguros de No Vida, abarcando algunos los métodos más usados en la industria aseguradora tradicional. Mi único interés es el divulgativo y el de mi propio aprendizaje en el trascurso del desarrollo de este proyecto, dedicando únicamente parte de mi tiempo libre. Por tanto, es posible la presencia (espero que pocos, jeje) de errores tanto técnicos como de programación en este documento.
import warnings
warnings.filterwarnings("ignore", category=FutureWarning)
from base import *
import triangles as tr
import dev_factor as devf
#import base
import tail_factor as tailf
import deterministic as dt
import tests_cl as test
import cashflows as cf
#import ReservMan as resm
#import chain ladder as cl #No se hará uso de esta herramienta en este documento.
import pandas as pd
import numpy as np
from openpyxl import load_workbook
from datetime import datetime
import plotly.express as px
import plotly.graph_objects as go
from plotly.subplots import make_subplots
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score
from scipy.stats import pearsonr
Vamos a hacer uso de un dataset que integra ya el paquete chainladder, y que recoge datos de siniestralidad de diferentes compañías de seguros en los Estados Unidos para diferentes LoB.
https://raw.githubusercontent.com/casact/chainladder-python/master/chainladder/utils/data/clrd.csv
#Lectura de documento .csv
data = pd.read_csv('Data/Claims.csv')
#Información y muestra de los datos importados
data.info()
data.head()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 42845 entries, 0 to 42844 Data columns (total 14 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 GRCODE 42845 non-null int64 1 GRNAME 42845 non-null object 2 AccidentYear 42845 non-null int64 3 DevelopmentYear 42845 non-null int64 4 DevelopmentLag 42845 non-null int64 5 IncurLoss 42845 non-null int64 6 CumPaidLoss 42845 non-null int64 7 BulkLoss 42845 non-null int64 8 EarnedPremDIR 42845 non-null int64 9 EarnedPremCeded 42845 non-null int64 10 EarnedPremNet 42845 non-null int64 11 Single 42845 non-null int64 12 PostedReserve97 42845 non-null int64 13 LOB 42845 non-null object dtypes: int64(12), object(2) memory usage: 4.6+ MB
| GRCODE | GRNAME | AccidentYear | DevelopmentYear | DevelopmentLag | IncurLoss | CumPaidLoss | BulkLoss | EarnedPremDIR | EarnedPremCeded | EarnedPremNet | Single | PostedReserve97 | LOB | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 86 | Allstate Ins Co Grp | 1988 | 1988 | 1 | 367404 | 70571 | 127737 | 400699 | 5957 | 394742 | 0 | 281872 | wkcomp |
| 1 | 86 | Allstate Ins Co Grp | 1988 | 1989 | 2 | 362988 | 155905 | 60173 | 400699 | 5957 | 394742 | 0 | 281872 | wkcomp |
| 2 | 86 | Allstate Ins Co Grp | 1988 | 1990 | 3 | 347288 | 220744 | 27763 | 400699 | 5957 | 394742 | 0 | 281872 | wkcomp |
| 3 | 86 | Allstate Ins Co Grp | 1988 | 1991 | 4 | 330648 | 251595 | 15280 | 400699 | 5957 | 394742 | 0 | 281872 | wkcomp |
| 4 | 86 | Allstate Ins Co Grp | 1988 | 1992 | 5 | 354690 | 274156 | 27689 | 400699 | 5957 | 394742 | 0 | 281872 | wkcomp |
Los datos que nos van a interesar para nuestro análisis son:
A continuación, se van a contruir, a partir de esta bbdd los triángulos para pagos acumulados y coste incurrido para las LoB de ppauto y othliab. Incluiremos los datos de todas las compañías, ya que al tratarse de un trabajo ilustrativo, dispondremos de un volumen mayor de datos.
#Triángulos de LoB ppauto
triang_CumPaid_ppauto = upload_triangle_from_csv(file='Data/Claims.csv',
base_period='AccidentYear',
dev_period='DevelopmentLag',
aggr_values='CumPaidLoss',
lob_column='LOB',
lob_name='ppauto',
type_triangle='CumPayments')
triang_IncLoss_ppauto = upload_triangle_from_csv('Data/Claims.csv', 'AccidentYear', 'DevelopmentLag', 'IncurLoss', 'LOB', 'ppauto', 'Incurred')
#Triángulos de LoB othliab
triang_CumPaid_othliab = upload_triangle_from_csv('Data/Claims.csv', 'AccidentYear', 'DevelopmentLag', 'CumPaidLoss', 'LOB', 'othliab', 'CumPayments')
triang_IncLoss_othliab = upload_triangle_from_csv('Data/Claims.csv', 'AccidentYear', 'DevelopmentLag', 'IncurLoss', 'LOB', 'othliab', 'Incurred')
#Muestra del Output:
triang_CumPaid_ppauto.show()
| DevelopmentLag | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||
| 1988 | 3,092,818.00 | 5,942,711.00 | 7,239,089.00 | 7,930,109.00 | 8,318,795.00 | 8,518,201.00 | 8,610,355.00 | 8,655,509.00 | 8,682,451.00 | 8,690,036.00 |
| 1989 | 3,556,683.00 | 6,753,435.00 | 8,219,551.00 | 9,018,288.00 | 9,441,842.00 | 9,647,917.00 | 9,753,014.00 | 9,800,477.00 | 9,823,747.00 | nan |
| 1990 | 4,015,052.00 | 7,478,257.00 | 9,094,949.00 | 9,945,288.00 | 10,371,175.00 | 10,575,467.00 | 10,671,988.00 | 10,728,411.00 | nan | nan |
| 1991 | 4,065,571.00 | 7,564,284.00 | 9,161,104.00 | 10,006,407.00 | 10,419,901.00 | 10,612,083.00 | 10,713,621.00 | nan | nan | nan |
| 1992 | 4,551,591.00 | 8,344,021.00 | 10,047,179.00 | 10,901,995.00 | 11,336,777.00 | 11,555,121.00 | nan | nan | nan | nan |
| 1993 | 5,020,277.00 | 9,125,734.00 | 10,890,282.00 | 11,782,219.00 | 12,249,826.00 | nan | nan | nan | nan | nan |
| 1994 | 5,569,355.00 | 9,871,002.00 | 11,641,397.00 | 12,600,432.00 | nan | nan | nan | nan | nan | nan |
| 1995 | 5,803,124.00 | 10,008,734.00 | 11,807,279.00 | nan | nan | nan | nan | nan | nan | nan |
| 1996 | 5,835,368.00 | 9,900,842.00 | nan | nan | nan | nan | nan | nan | nan | nan |
| 1997 | 5,754,249.00 | nan | nan | nan | nan | nan | nan | nan | nan | nan |
Se muestra a continuación la lectura del primero de los triángulos, a modo ilustrativo, en caso que se dispusiera del triángulo construido en un fichero .xlsx:
## TRIÁNGULO PAGOS ACUMULADOS
triang_CumPaid_ppauto = upload_triangle_from_excel(file = "Data/Triangles.xlsx",
sheet = "0_Datos de entrada",
init_col = 3,
init_row = 12,
dim = 14,
start_year=2008,
month=12,
periodicity='annual',
type_triangle='CumPayments')
triang_CumPaid_ppauto.show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||
| 12/2008 | 59,769,792.25 | 165,450,290.25 | 199,870,725.25 | 217,710,186.75 | 226,508,362.50 | 231,561,596.00 | 234,583,184.50 | 235,492,526.50 | 235,842,953.50 | 236,679,451.75 | 236,830,634.25 | 237,088,328.75 | 237,137,708.50 | 237,139,707.00 |
| 12/2009 | 66,322,949.00 | 172,599,974.75 | 202,734,288.75 | 219,299,874.50 | 229,098,212.00 | 233,612,156.75 | 235,362,048.25 | 236,241,391.75 | 236,582,442.25 | 236,978,784.00 | 237,011,082.00 | 237,220,333.00 | 237,241,838.75 | nan |
| 12/2010 | 65,872,992.50 | 171,545,542.00 | 204,518,830.25 | 219,677,340.75 | 228,315,913.00 | 230,619,957.75 | 232,128,895.25 | 233,760,436.00 | 234,838,481.50 | 235,400,644.50 | 235,481,167.25 | 236,568,641.75 | nan | nan |
| 12/2011 | 73,281,092.50 | 177,437,692.25 | 211,989,349.25 | 225,904,938.00 | 233,299,603.25 | 237,212,167.50 | 238,171,038.00 | 238,204,519.00 | 239,276,107.00 | 239,329,410.25 | 239,647,219.00 | nan | nan | nan |
| 12/2012 | 71,133,350.75 | 170,462,076.75 | 202,128,321.50 | 215,426,247.75 | 220,361,960.00 | 223,714,366.75 | 224,830,359.25 | 225,441,690.25 | 225,710,275.00 | 225,835,380.75 | nan | nan | nan | nan |
| 12/2013 | 73,052,085.75 | 169,312,321.50 | 196,125,924.75 | 205,648,105.25 | 209,351,135.00 | 210,680,426.25 | 212,484,079.50 | 213,326,428.00 | 213,720,710.00 | nan | nan | nan | nan | nan |
| 12/2014 | 80,029,486.25 | 167,411,221.25 | 191,426,151.00 | 202,659,814.00 | 207,440,765.00 | 209,990,095.00 | 211,954,827.00 | 213,343,348.75 | nan | nan | nan | nan | nan | nan |
| 12/2015 | 79,283,232.00 | 163,188,432.75 | 194,775,049.00 | 213,604,716.50 | 221,803,863.75 | 226,107,304.50 | 228,078,954.25 | nan | nan | nan | nan | nan | nan | nan |
| 12/2016 | 76,831,315.75 | 149,990,867.25 | 176,481,879.00 | 194,354,543.25 | 203,591,533.25 | 207,264,256.50 | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2017 | 72,758,633.50 | 153,658,485.75 | 182,026,017.25 | 201,342,186.50 | 210,461,641.25 | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2018 | 75,059,369.00 | 153,899,163.25 | 185,599,785.00 | 200,289,790.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2019 | 80,575,836.25 | 161,348,381.25 | 192,301,457.25 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2020 | 52,497,772.25 | 108,637,212.25 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2021 | 70,453,787.25 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
## TRIÁNGULO DE INCURRIDO
triang_Incurred_ppauto = upload_triangle_from_excel(file = "Data/Triangles.xlsx",
sheet = "0_Datos de entrada",
init_col = 3,
init_row = 46,
dim = 14,
start_year=2008,
month=12,
periodicity='annual',
type_triangle='Incurred')
triang_Incurred_ppauto.show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||
| 12/2008 | 160,139,045.50 | 226,559,737.25 | 236,266,268.00 | 244,960,152.50 | 243,214,489.00 | 242,232,361.00 | 237,986,488.25 | 237,402,737.25 | 237,520,052.00 | 237,846,378.00 | 237,655,232.50 | 237,107,363.50 | 237,137,708.50 | 237,139,707.00 |
| 12/2009 | 170,668,596.00 | 229,474,322.00 | 241,053,886.50 | 247,883,002.50 | 246,231,580.00 | 242,918,107.25 | 241,458,780.50 | 240,670,060.75 | 240,441,831.00 | 238,746,816.00 | 238,458,078.25 | 238,656,180.00 | 238,669,835.25 | nan |
| 12/2010 | 172,718,677.25 | 231,355,591.25 | 243,742,133.25 | 244,439,980.75 | 241,871,707.00 | 240,849,518.00 | 239,921,955.00 | 239,826,406.75 | 239,671,876.50 | 239,397,733.75 | 238,663,761.00 | 237,407,042.25 | nan | nan |
| 12/2011 | 183,979,363.75 | 241,276,966.00 | 249,143,599.25 | 249,556,895.00 | 247,601,653.25 | 244,683,960.50 | 243,566,232.00 | 243,056,439.50 | 241,679,172.00 | 242,572,099.00 | 243,090,398.25 | nan | nan | nan |
| 12/2012 | 175,627,597.25 | 226,648,257.50 | 238,413,819.00 | 234,372,948.25 | 232,489,365.50 | 228,558,839.25 | 227,516,628.50 | 226,527,089.25 | 226,508,345.00 | 226,246,170.50 | nan | nan | nan | nan |
| 12/2013 | 177,484,462.75 | 223,476,284.50 | 223,127,831.50 | 221,309,161.50 | 219,625,833.00 | 217,998,572.75 | 219,304,239.00 | 218,348,907.00 | 218,296,573.25 | nan | nan | nan | nan | nan |
| 12/2014 | 192,433,529.75 | 224,730,010.75 | 226,156,647.50 | 222,911,496.50 | 221,214,136.50 | 221,192,476.75 | 220,667,758.50 | 219,193,220.75 | nan | nan | nan | nan | nan | nan |
| 12/2015 | 195,675,030.25 | 248,325,743.75 | 250,155,328.50 | 243,339,946.50 | 240,425,484.25 | 237,945,648.50 | 239,437,836.75 | nan | nan | nan | nan | nan | nan | nan |
| 12/2016 | 195,320,417.25 | 231,643,347.25 | 237,312,493.25 | 235,702,867.75 | 232,689,189.25 | 234,761,751.00 | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2017 | 193,690,346.50 | 241,381,936.25 | 248,638,909.75 | 245,126,638.75 | 247,774,394.00 | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2018 | 194,260,377.50 | 241,752,892.50 | 248,933,149.50 | 248,301,831.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2019 | 204,718,780.00 | 258,748,269.50 | 269,575,517.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2020 | 137,506,664.75 | 178,589,862.50 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2021 | 189,587,392.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
## TRIANGULO DE RESERVA CASO A CASO
triang_Reserve_ppauto = upload_triangle_from_excel(file = "Data/Triangles.xlsx",
sheet = "0_Datos de entrada",
init_col = 3,
init_row = 29,
dim = 14,
start_year=2008,
month=12,
periodicity='annual',
type_triangle='CaseReserves')
triang_Reserve_ppauto.show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||
| 12/2008 | 100,369,253.25 | 61,109,447.00 | 36,395,542.75 | 27,249,965.75 | 16,706,126.50 | 10,670,765.00 | 3,403,303.75 | 1,910,210.75 | 1,677,098.50 | 1,166,926.25 | 824,598.25 | 19,034.75 | 0.00 | 0.00 |
| 12/2009 | 104,345,647.00 | 56,874,347.25 | 38,319,597.75 | 28,583,128.00 | 17,133,368.00 | 9,305,950.50 | 6,096,732.25 | 4,428,669.00 | 3,859,388.75 | 1,768,032.00 | 1,446,996.25 | 1,435,847.00 | 1,427,996.50 | nan |
| 12/2010 | 106,845,684.75 | 59,810,049.25 | 39,223,303.00 | 24,762,640.00 | 13,555,794.00 | 10,229,560.25 | 7,793,059.75 | 6,065,970.75 | 4,833,395.00 | 3,997,089.25 | 3,182,593.75 | 838,400.50 | nan | nan |
| 12/2011 | 110,698,271.25 | 63,839,273.75 | 37,154,250.00 | 23,651,957.00 | 14,302,050.00 | 7,471,793.00 | 5,395,194.00 | 4,851,920.50 | 2,403,065.00 | 3,242,688.75 | 3,443,179.25 | nan | nan | nan |
| 12/2012 | 104,494,246.50 | 56,186,180.75 | 36,285,497.50 | 18,946,700.50 | 12,127,405.50 | 4,844,472.50 | 2,686,269.25 | 1,085,399.00 | 798,070.00 | 410,789.75 | nan | nan | nan | nan |
| 12/2013 | 104,432,377.00 | 54,163,963.00 | 27,001,906.75 | 15,661,056.25 | 10,274,698.00 | 7,318,146.50 | 6,820,159.50 | 5,022,479.00 | 4,575,863.25 | nan | nan | nan | nan | nan |
| 12/2014 | 112,404,043.50 | 57,318,789.50 | 34,730,496.50 | 20,251,682.50 | 13,773,371.50 | 11,202,381.75 | 8,712,931.50 | 5,849,872.00 | nan | nan | nan | nan | nan | nan |
| 12/2015 | 116,391,798.25 | 85,137,311.00 | 55,380,279.50 | 29,735,230.00 | 18,621,620.50 | 11,838,344.00 | 11,358,882.50 | nan | nan | nan | nan | nan | nan | nan |
| 12/2016 | 118,489,101.50 | 81,652,480.00 | 60,830,614.25 | 41,348,324.50 | 29,097,656.00 | 27,497,494.50 | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2017 | 120,931,713.00 | 87,723,450.50 | 66,612,892.50 | 43,784,452.25 | 37,312,752.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2018 | 119,201,008.50 | 87,853,729.25 | 63,333,364.50 | 48,012,041.00 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2019 | 124,142,943.75 | 97,399,888.25 | 77,274,060.50 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2020 | 85,008,892.50 | 69,952,650.25 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2021 | 119,133,605.50 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
CumPaid_tr = triang_CumPaid_ppauto
Incurred_tr = triang_Incurred_ppauto
CaseRes_tr = triang_Reserve_ppauto
Incurred_tr.show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||
| 12/2008 | 160,139,045.50 | 226,559,737.25 | 236,266,268.00 | 244,960,152.50 | 243,214,489.00 | 242,232,361.00 | 237,986,488.25 | 237,402,737.25 | 237,520,052.00 | 237,846,378.00 | 237,655,232.50 | 237,107,363.50 | 237,137,708.50 | 237,139,707.00 |
| 12/2009 | 170,668,596.00 | 229,474,322.00 | 241,053,886.50 | 247,883,002.50 | 246,231,580.00 | 242,918,107.25 | 241,458,780.50 | 240,670,060.75 | 240,441,831.00 | 238,746,816.00 | 238,458,078.25 | 238,656,180.00 | 238,669,835.25 | nan |
| 12/2010 | 172,718,677.25 | 231,355,591.25 | 243,742,133.25 | 244,439,980.75 | 241,871,707.00 | 240,849,518.00 | 239,921,955.00 | 239,826,406.75 | 239,671,876.50 | 239,397,733.75 | 238,663,761.00 | 237,407,042.25 | nan | nan |
| 12/2011 | 183,979,363.75 | 241,276,966.00 | 249,143,599.25 | 249,556,895.00 | 247,601,653.25 | 244,683,960.50 | 243,566,232.00 | 243,056,439.50 | 241,679,172.00 | 242,572,099.00 | 243,090,398.25 | nan | nan | nan |
| 12/2012 | 175,627,597.25 | 226,648,257.50 | 238,413,819.00 | 234,372,948.25 | 232,489,365.50 | 228,558,839.25 | 227,516,628.50 | 226,527,089.25 | 226,508,345.00 | 226,246,170.50 | nan | nan | nan | nan |
| 12/2013 | 177,484,462.75 | 223,476,284.50 | 223,127,831.50 | 221,309,161.50 | 219,625,833.00 | 217,998,572.75 | 219,304,239.00 | 218,348,907.00 | 218,296,573.25 | nan | nan | nan | nan | nan |
| 12/2014 | 192,433,529.75 | 224,730,010.75 | 226,156,647.50 | 222,911,496.50 | 221,214,136.50 | 221,192,476.75 | 220,667,758.50 | 219,193,220.75 | nan | nan | nan | nan | nan | nan |
| 12/2015 | 195,675,030.25 | 248,325,743.75 | 250,155,328.50 | 243,339,946.50 | 240,425,484.25 | 237,945,648.50 | 239,437,836.75 | nan | nan | nan | nan | nan | nan | nan |
| 12/2016 | 195,320,417.25 | 231,643,347.25 | 237,312,493.25 | 235,702,867.75 | 232,689,189.25 | 234,761,751.00 | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2017 | 193,690,346.50 | 241,381,936.25 | 248,638,909.75 | 245,126,638.75 | 247,774,394.00 | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2018 | 194,260,377.50 | 241,752,892.50 | 248,933,149.50 | 248,301,831.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2019 | 204,718,780.00 | 258,748,269.50 | 269,575,517.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2020 | 137,506,664.75 | 178,589,862.50 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2021 | 189,587,392.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
Incurred_tr.show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||
| 12/2008 | 160,139,045.50 | 226,559,737.25 | 236,266,268.00 | 244,960,152.50 | 243,214,489.00 | 242,232,361.00 | 237,986,488.25 | 237,402,737.25 | 237,520,052.00 | 237,846,378.00 | 237,655,232.50 | 237,107,363.50 | 237,137,708.50 | 237,139,707.00 |
| 12/2009 | 170,668,596.00 | 229,474,322.00 | 241,053,886.50 | 247,883,002.50 | 246,231,580.00 | 242,918,107.25 | 241,458,780.50 | 240,670,060.75 | 240,441,831.00 | 238,746,816.00 | 238,458,078.25 | 238,656,180.00 | 238,669,835.25 | nan |
| 12/2010 | 172,718,677.25 | 231,355,591.25 | 243,742,133.25 | 244,439,980.75 | 241,871,707.00 | 240,849,518.00 | 239,921,955.00 | 239,826,406.75 | 239,671,876.50 | 239,397,733.75 | 238,663,761.00 | 237,407,042.25 | nan | nan |
| 12/2011 | 183,979,363.75 | 241,276,966.00 | 249,143,599.25 | 249,556,895.00 | 247,601,653.25 | 244,683,960.50 | 243,566,232.00 | 243,056,439.50 | 241,679,172.00 | 242,572,099.00 | 243,090,398.25 | nan | nan | nan |
| 12/2012 | 175,627,597.25 | 226,648,257.50 | 238,413,819.00 | 234,372,948.25 | 232,489,365.50 | 228,558,839.25 | 227,516,628.50 | 226,527,089.25 | 226,508,345.00 | 226,246,170.50 | nan | nan | nan | nan |
| 12/2013 | 177,484,462.75 | 223,476,284.50 | 223,127,831.50 | 221,309,161.50 | 219,625,833.00 | 217,998,572.75 | 219,304,239.00 | 218,348,907.00 | 218,296,573.25 | nan | nan | nan | nan | nan |
| 12/2014 | 192,433,529.75 | 224,730,010.75 | 226,156,647.50 | 222,911,496.50 | 221,214,136.50 | 221,192,476.75 | 220,667,758.50 | 219,193,220.75 | nan | nan | nan | nan | nan | nan |
| 12/2015 | 195,675,030.25 | 248,325,743.75 | 250,155,328.50 | 243,339,946.50 | 240,425,484.25 | 237,945,648.50 | 239,437,836.75 | nan | nan | nan | nan | nan | nan | nan |
| 12/2016 | 195,320,417.25 | 231,643,347.25 | 237,312,493.25 | 235,702,867.75 | 232,689,189.25 | 234,761,751.00 | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2017 | 193,690,346.50 | 241,381,936.25 | 248,638,909.75 | 245,126,638.75 | 247,774,394.00 | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2018 | 194,260,377.50 | 241,752,892.50 | 248,933,149.50 | 248,301,831.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2019 | 204,718,780.00 | 258,748,269.50 | 269,575,517.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2020 | 137,506,664.75 | 178,589,862.50 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2021 | 189,587,392.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
Antes de llevar a cabo ninguna proyección, es una buena opción, y más en Python, poder hacer una análisis visual del triángulo.
Para mostrar los gráficos, usaremos la libería plotly.express, si bien se pueden usar otras con un diseño más atractivo, nos decantamos por esta porque nos permite un análisis del gráfico de forma más interactiva.
A continuación veremos de forma gráfica el desarrollo de los pagos acumulados por año de accidente:
#Grafico por año de accidente y año de desarrollo del triangulo de pagos acumulados:
CumPaid_tr.graph_tr()
#Grafico por año de accidente y año de desarrollo del triangulo de Coste Incurrido:
Incurred_tr.graph_tr()
Como se observa en el gráfico anterior, los pagos de este triángulo se desarrollan de forma creciente, sin observar recobros en ningún periodo de desarrollo.
Al igual que se ha analizado el triángulo de pagos acumulado, también se podría hacer lo mismo con el triángulo de pagos incremental.
Si bien puede que no dispongamos directamente de él (o viceversa), se crean dos funciones, una para el paso de un triángulo de pagos incrementales a acumulados, y otra para el paso de triángulos acumulados a incrementales. Esta última función la aplicaremos a continución para obtener una triángulo incremental que podamos analizar.
Con las funciones de transformación creadas, podremos obtener de forma simple el triángulo de pagos incremental que podríamos analizar.
triang_IncrPaid_ppauto = CumPaid_tr.to_incr()
triang_IncrPaid_ppauto.show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||
| 12/2008 | 59,769,792.25 | 105,680,498.00 | 34,420,435.00 | 17,839,461.50 | 8,798,175.75 | 5,053,233.50 | 3,021,588.50 | 909,342.00 | 350,427.00 | 836,498.25 | 151,182.50 | 257,694.50 | 49,379.75 | 1,998.50 |
| 12/2009 | 66,322,949.00 | 106,277,025.75 | 30,134,314.00 | 16,565,585.75 | 9,798,337.50 | 4,513,944.75 | 1,749,891.50 | 879,343.50 | 341,050.50 | 396,341.75 | 32,298.00 | 209,251.00 | 21,505.75 | nan |
| 12/2010 | 65,872,992.50 | 105,672,549.50 | 32,973,288.25 | 15,158,510.50 | 8,638,572.25 | 2,304,044.75 | 1,508,937.50 | 1,631,540.75 | 1,078,045.50 | 562,163.00 | 80,522.75 | 1,087,474.50 | nan | nan |
| 12/2011 | 73,281,092.50 | 104,156,599.75 | 34,551,657.00 | 13,915,588.75 | 7,394,665.25 | 3,912,564.25 | 958,870.50 | 33,481.00 | 1,071,588.00 | 53,303.25 | 317,808.75 | nan | nan | nan |
| 12/2012 | 71,133,350.75 | 99,328,726.00 | 31,666,244.75 | 13,297,926.25 | 4,935,712.25 | 3,352,406.75 | 1,115,992.50 | 611,331.00 | 268,584.75 | 125,105.75 | nan | nan | nan | nan |
| 12/2013 | 73,052,085.75 | 96,260,235.75 | 26,813,603.25 | 9,522,180.50 | 3,703,029.75 | 1,329,291.25 | 1,803,653.25 | 842,348.50 | 394,282.00 | nan | nan | nan | nan | nan |
| 12/2014 | 80,029,486.25 | 87,381,735.00 | 24,014,929.75 | 11,233,663.00 | 4,780,951.00 | 2,549,330.00 | 1,964,732.00 | 1,388,521.75 | nan | nan | nan | nan | nan | nan |
| 12/2015 | 79,283,232.00 | 83,905,200.75 | 31,586,616.25 | 18,829,667.50 | 8,199,147.25 | 4,303,440.75 | 1,971,649.75 | nan | nan | nan | nan | nan | nan | nan |
| 12/2016 | 76,831,315.75 | 73,159,551.50 | 26,491,011.75 | 17,872,664.25 | 9,236,990.00 | 3,672,723.25 | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2017 | 72,758,633.50 | 80,899,852.25 | 28,367,531.50 | 19,316,169.25 | 9,119,454.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2018 | 75,059,369.00 | 78,839,794.25 | 31,700,621.75 | 14,690,005.75 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2019 | 80,575,836.25 | 80,772,545.00 | 30,953,076.00 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2020 | 52,497,772.25 | 56,139,440.00 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
| 12/2021 | 70,453,787.25 | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan | nan |
# Asignamos el nuevo triangulo a su clase correspondiente:
IncPaid_tr = CumPaid_tr.to_incr()
#Grafico por año de accidente y año de desarrollo del triangulo de Pagos incremental:
IncPaid_tr.graph_tr()
Creamos una función para el cálculo de los factores de paso, que también nos servirá en el futuro para cualquier otro triángulo.
Aplicamos la función para obtener los factores de paso sobre el triángulo de coste incurrido:
linkf_incurred = Incurred_tr.link_factors()
linkf_incurred
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | |||||||||||||
| 12/2008 | 1.414769 | 1.042843 | 1.036797 | 0.992874 | 0.995962 | 0.982472 | 0.997547 | 1.000494 | 1.001374 | 0.999196 | 0.997695 | 1.000128 | 1.000008 |
| 12/2009 | 1.344561 | 1.050461 | 1.028330 | 0.993338 | 0.986543 | 0.993993 | 0.996734 | 0.999052 | 0.992950 | 0.998791 | 1.000831 | 1.000057 | NaN |
| 12/2010 | 1.339494 | 1.053539 | 1.002863 | 0.989493 | 0.995774 | 0.996149 | 0.999602 | 0.999356 | 0.998856 | 0.996934 | 0.994734 | NaN | NaN |
| 12/2011 | 1.311435 | 1.032604 | 1.001659 | 0.992165 | 0.988216 | 0.995432 | 0.997907 | 0.994334 | 1.003695 | 1.002137 | NaN | NaN | NaN |
| 12/2012 | 1.290505 | 1.051911 | 0.983051 | 0.991963 | 0.983094 | 0.995440 | 0.995651 | 0.999917 | 0.998843 | NaN | NaN | NaN | NaN |
| 12/2013 | 1.259132 | 0.998441 | 0.991849 | 0.992394 | 0.992591 | 1.005989 | 0.995644 | 0.999760 | NaN | NaN | NaN | NaN | NaN |
| 12/2014 | 1.167832 | 1.006348 | 0.985651 | 0.992385 | 0.999902 | 0.997628 | 0.993318 | NaN | NaN | NaN | NaN | NaN | NaN |
| 12/2015 | 1.269072 | 1.007368 | 0.972755 | 0.988023 | 0.989686 | 1.006271 | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 12/2016 | 1.185966 | 1.024474 | 0.993217 | 0.987214 | 1.008907 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 12/2017 | 1.246226 | 1.030064 | 0.985874 | 1.010802 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 12/2018 | 1.244479 | 1.029701 | 0.997464 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 12/2019 | 1.263921 | 1.041845 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 12/2020 | 1.298772 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
Para una mejor interpretación de la matriz de factores, podemos aplicarle un mapa de calor:
# Ultilizamos la libreria de seaborn para mostrar de forma más visual los factores de paso
Incurred_tr.heatmap_linkf()
# Gráfico por año de accidente de los Link factors:
Incurred_tr.graph_linkf()
A continuación creamos los factores de desarrollo, mediante la metodología Chain-Ladder, ampliamente usada en la industria aseguradora, mediante el cálculo de un desarrollo por promedio ponderado o Weight-Average.
En este momento, vamos a llevar a cabo un cálculo rápido sin ignorar factores, más adelante mostraremos cómo ignorar factores de paso, y cómo estimar el factor de desarrollo mediante otra formulación.
Incurred_tr.get_dev_f(method='vol_weight', cal_y_ignore=0, acc_y_ignore=0, f_ignore=None)
dev_f([1.2759893 , 1.03084414, 0.99809336, 0.99310963, 0.99330834,
0.99652545, 0.99668968, 0.99878094, 0.99914652, 0.99927438,
0.99775247, 1.00009248, 1.00000843])
incurred_df = Incurred_tr.get_dev_f(method='vol_weight', cal_y_ignore=0, acc_y_ignore=0, f_ignore=None)
CumPaid_df = CumPaid_tr.get_dev_f(method='vol_weight', cal_y_ignore=0, acc_y_ignore=0, f_ignore=None)
CumPaid_df
dev_f([2.25041973, 1.18401686, 1.07833649, 1.03526378, 1.01565382,
1.00781554, 1.0039609 , 1.00253458, 1.00168344, 1.00061347,
1.00219141, 1.00014945, 1.00000843])
Incurred_tr.get_dev_f(method='vol_weight', cal_y_ignore=0, acc_y_ignore=0, f_ignore=None).graph_df()
A parte de esta metodología, que es la más usada, para obtener los factores de desarrollo, existen otras metodologías. Aquí vamos a formularlas, incluyendo la opción de ignorar factores de paso, bien por año de calendario o por año de accidente.
En primer lugar, vamos a contruir una función que devuelva un triángulo con los pesos que se quiera dar a cada uno de los factores de paso. Los valores serán 1 o 0 en función de si deseamos tener esos factores de paso en cuenta o no.
En el ejemplo de uso de la función, creamos unos pesos que ignoren los cuatro primeros años de calendario y el primer año de accidente.
Una vez definida un triángulo que contenga los pesos que queremos otorgar a cada factor de paso, podremos crear una función que permita calcular los factores de desarrollo mediante distintas metodologías y con la opción de poder ignorar diferentes factores.
Las distintas metodologías que incorporaremos son:
Dentro de los inputs de la función se podrán incorporar también los periodos de calendario y/o de accidente que se desean ignorar del cálculo.
Con las funciones creadas anteriores, se puede ver rapidamente una comparativa de los factores de desarrollo resultantes en cada caso:
Incurred_tr.get_dev_f(method='all', cal_y_ignore=0, acc_y_ignore=0, f_ignore=None)
dev_f([[1.27970479, 1.2759893 , 1.25911133, 1.26907221, 1.27814917,
1.27759651, 1.16783188, 1.41476888],
[1.03079989, 1.03084414, 1.02741191, 1.03133422, 1.03064324,
1.0317619 , 0.99844076, 1.05353898],
[0.99813735, 0.99809336, 0.99130955, 0.99321727, 0.99797142,
0.99666205, 0.9727554 , 1.03679698],
[0.99306513, 0.99310963, 0.99408536, 0.99227532, 0.99304566,
0.99157945, 0.98721408, 1.01080158],
[0.99340827, 0.99330834, 0.99504912, 0.99259076, 0.99338098,
0.99266767, 0.98309374, 1.008907 ],
[0.99667168, 0.99652545, 0.99964808, 0.99579443, 0.99664705,
0.99743841, 0.9824719 , 1.00627113],
[0.99662881, 0.99668968, 0.99595673, 0.99673352, 0.99662708,
0.99669642, 0.99331784, 0.99960175],
[0.99881877, 0.99878094, 0.99867366, 0.99955799, 0.99881665,
0.99952123, 0.99433355, 1.00049416],
[0.99914354, 0.99914652, 0.99952231, 0.99885617, 0.9991371 ,
0.99969087, 0.99295042, 1.00369468],
[0.99926443, 0.99927438, 0.99961266, 0.99899348, 0.99926269,
0.99899348, 0.99693409, 1.00213668],
[0.99775327, 0.99775247, 0.99725988, 0.99769469, 0.99775016,
0.99769469, 0.99473435, 1.00083076],
[1.0000926 , 1.00009248, 1.0000808 , 1.0000926 , 1.0000926 ,
1.0000926 , 1.00005722, 1.00012798],
[1.00000843, 1.00000843, 1.00000843, 1.00000843, 1.00000843,
1.00000843, 1.00000843, 1.00000843]])
Incurred_tr.get_dev_f(method='all', cal_y_ignore=0, acc_y_ignore=0, f_ignore=None).graph_df()
A continuación tomamos la media ponderada volume weight como los factores de desarrollo que usaremos e nuestro análisis.
Factors_to_ignore = [('12/2014', 1), ('12/2016', 1), ('12/2013', 2)]
df_incurred = Incurred_tr.get_dev_f(method='vol_weight', cal_y_ignore=0, acc_y_ignore=0, f_ignore=Factors_to_ignore)
df_incurred
dev_f([1.29551492, 1.03362726, 0.99809336, 0.99310963, 0.99330834,
0.99652545, 0.99668968, 0.99878094, 0.99914652, 0.99927438,
0.99775247, 1.00009248, 1.00000843])
Junto con los factores de desarrollo, es interesante revisar el producto de los factores de desarrollo, que nos muestra el acumulado de los factores de desarrollo. También se puede análizar cómo de desarrollado se encuentra el triángulo en cada caso mediante el inverso del producto de los factores de desarrollo. Conocer si el triángulo está muy desarrollado o no puede ser bastante últil a la hora de elegir que metodología es la más apropiada o no. Más adelante veremos esto con más detenimiento.
df_incurred.cdf()
[1.3030407096526313, 1.0058091069747748, 0.9730868588597307, 0.9749457298937636, 0.9817100791901537, 0.9883236015620764, 0.9917695497808868, 0.9950635295057482, 0.9962780505467228, 0.9971290840671657, 0.997853150690959, 1.0001009118138537, 1.0000084275926113]
df_incurred.inv_df()
[0.7674357313568377, 0.9942244438487466, 1.0276574911018799, 1.0256981176880138, 1.0186306743686835, 1.0118143474662233, 1.0082987526900091, 1.0049609601275447, 1.0037358541134522, 1.0028791818218, 1.0021514681870318, 0.9998990983683129, 0.9999915724784124]
Es posible crear un factor de desarrollo personalizado en base a otros factores de desarrollo o crear uno nuevo. Se utiliza la siguiente función:
vol_f = Incurred_tr.get_dev_f(method='vol_weight', cal_y_ignore=0, acc_y_ignore=0, f_ignore=Factors_to_ignore)
time_f = Incurred_tr.get_dev_f(method='time_weight', cal_y_ignore=0, acc_y_ignore=0, f_ignore=Factors_to_ignore)
avg_f = Incurred_tr.get_dev_f(method='avg', cal_y_ignore=0, acc_y_ignore=0, f_ignore=Factors_to_ignore)
vol_f
dev_f([1.29551492, 1.03362726, 0.99809336, 0.99310963, 0.99330834,
0.99652545, 0.99668968, 0.99878094, 0.99914652, 0.99927438,
0.99775247, 1.00009248, 1.00000843])
new_factor = custom_devf(vol_f, vol_f, vol_f, avg_f, avg_f, time_f, vol_f, vol_f, 1.1, 1, 1, 1, 1)
new_factor
dev_f([1.29551492, 1.03362726, 0.99809336, 0.99306513, 0.99340827,
0.99964808, 0.99668968, 0.99878094, 1.1 , 1. ,
1. , 1. , 1. ])
En ciertos casos, podemos presenciar triángulos en los que, bien porque se trate de un negocio de desarrollo lento (como pudieran ser seguros de RC Corporal en los seguros de auto), o bien porque la experiencia de la compañía aún sea pequeña, se presente un array en los factores de dasarrollo incompleto. Esto se puede dar en casos en los que el último periodo en el factor de desarrollo no presente una cifra cercana a 1.
En el caso que estamos observando, no vemos esa problematica, sin embargo, debemos conocer como poder solucionarlo. Para estos casos, se suele recurrir a la estimación de factores cola, proyectados a futuro en base a una distribución teórica. Las más utilizadas son la Potencia Inversa, Exponencial, Potencial o Weibull.
El cálculo de los factores se basan en el cálculo de un modelo de regresión, mediante el cuál, podamos estimar el factor de desarrollo en un periodo dado, en función del periodo en el que nos encontremos. Los factores y los periodos se ajustan a una distribución teórica para aplicar el modelo. Así, podemos obtener cuál sería el factor de desarrollo en periodos más allá de los que podemos calcular con la experiencia conocida.
Para poder calcular de forma sencilla los factores cola (también factores anteriores a la cola), hemos contruido la función dist_adj_factor. Los parametros que recibirá de input está función son:
Los outputs que devolverá la función serán:
Con la información que nos devuelve la función, podemos tener una mejor perspectiva de qué distribución se ajusta mejor al disponer de los coeficientes $R^2$.
Por ello, es interesante que, llegado el caso, podamos comparar de forma rápida el ajuste que mejor explica el desarrollo de los siniestros. Por ello, se diseña la siguiente función que permite de forma rápida ver los factores de desarrollo elegidos, junto con los factores ajustados mediante una distribución teórica y el coeficiente $R^2$ de cada una de ellas.
df_incurred.tail_f(distribution='all', only_tail=1, num_factors=4)
'Exponential'
La primera fila muestra los factores cola estimados, la segunda muestra el producto de los factores estimados, mientras que las dos últimas muestran los $R^2$ y $R^2 Adj.$
A continuación, mostramos los resulatados para la Weibull, que tiene un mayor $R^2$.
df_incurred.graph_tail_f(distribution='all', num_factors=4)
df_incurred.graph_tail_f(distribution='weibull', num_factors=4)
En este caso en particular, se observa como el producto de los factores cola estimados son bastante
weibull_f= df_incurred.tail_f(distribution='weibull', only_tail=1, num_factors=4)
weibull_f
array([1.00000875, 1.0000048 , 1.00000266, 1.00000149])
Incurred_tr.tests_cl(dev_f=incurred_df, test='linear')
Una de las metodologías más empleadas es el Chain-Ladder
Mediante el método chainladder, se puede proyectar un triángulo tanto de pagos como de incurrido, siempre que se introduzca un array de factores de desarrollo. Opcionalmente, también se puede incluir factores cola que se hayan definido anteriormente.
Incurr_devel = Incurred_tr.chainladder(dev_f = incurred_df, tail_f=weibull_f)
Incurr_devel.show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | Tail 1 | Tail 2 | Tail 3 | Tail 4 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||||||
| 12/2008 | 160,139,045.50 | 226,559,737.25 | 236,266,268.00 | 244,960,152.50 | 243,214,489.00 | 242,232,361.00 | 237,986,488.25 | 237,402,737.25 | 237,520,052.00 | 237,846,378.00 | 237,655,232.50 | 237,107,363.50 | 237,137,708.50 | 237,139,707.00 | 237,141,782.69 | 237,142,920.60 | 237,143,551.15 | 237,143,904.04 |
| 12/2009 | 170,668,596.00 | 229,474,322.00 | 241,053,886.50 | 247,883,002.50 | 246,231,580.00 | 242,918,107.25 | 241,458,780.50 | 240,670,060.75 | 240,441,831.00 | 238,746,816.00 | 238,458,078.25 | 238,656,180.00 | 238,669,835.25 | 238,671,846.66 | 238,673,935.77 | 238,675,081.03 | 238,675,715.65 | 238,676,070.82 |
| 12/2010 | 172,718,677.25 | 231,355,591.25 | 243,742,133.25 | 244,439,980.75 | 241,871,707.00 | 240,849,518.00 | 239,921,955.00 | 239,826,406.75 | 239,671,876.50 | 239,397,733.75 | 238,663,761.00 | 237,407,042.25 | 237,428,998.47 | 237,430,999.43 | 237,433,077.67 | 237,434,216.97 | 237,434,848.30 | 237,435,201.62 |
| 12/2011 | 183,979,363.75 | 241,276,966.00 | 249,143,599.25 | 249,556,895.00 | 247,601,653.25 | 244,683,960.50 | 243,566,232.00 | 243,056,439.50 | 241,679,172.00 | 242,572,099.00 | 243,090,398.25 | 242,544,044.24 | 242,566,475.55 | 242,568,519.80 | 242,570,643.01 | 242,571,806.97 | 242,572,451.95 | 242,572,812.92 |
| 12/2012 | 175,627,597.25 | 226,648,257.50 | 238,413,819.00 | 234,372,948.25 | 232,489,365.50 | 228,558,839.25 | 227,516,628.50 | 226,527,089.25 | 226,508,345.00 | 226,246,170.50 | 226,082,000.75 | 225,573,873.70 | 225,594,735.54 | 225,596,636.76 | 225,598,611.42 | 225,599,693.94 | 225,600,293.80 | 225,600,629.51 |
| 12/2013 | 177,484,462.75 | 223,476,284.50 | 223,127,831.50 | 221,309,161.50 | 219,625,833.00 | 217,998,572.75 | 219,304,239.00 | 218,348,907.00 | 218,296,573.25 | 218,110,260.66 | 217,951,994.53 | 217,462,139.94 | 217,482,251.59 | 217,484,084.44 | 217,485,988.09 | 217,487,031.68 | 217,487,609.97 | 217,487,933.60 |
| 12/2014 | 192,433,529.75 | 224,730,010.75 | 226,156,647.50 | 222,911,496.50 | 221,214,136.50 | 221,192,476.75 | 220,667,758.50 | 219,193,220.75 | 218,926,011.43 | 218,739,161.63 | 218,580,439.15 | 218,089,172.11 | 218,109,341.75 | 218,111,179.88 | 218,113,089.02 | 218,114,135.62 | 218,114,715.58 | 218,115,040.15 |
| 12/2015 | 195,675,030.25 | 248,325,743.75 | 250,155,328.50 | 243,339,946.50 | 240,425,484.25 | 237,945,648.50 | 239,437,836.75 | 238,645,220.64 | 238,354,298.20 | 238,150,866.67 | 237,978,058.58 | 237,443,194.73 | 237,465,154.29 | 237,467,155.55 | 237,469,234.11 | 237,470,373.59 | 237,471,005.02 | 237,471,358.39 |
| 12/2016 | 195,320,417.25 | 231,643,347.25 | 237,312,493.25 | 235,702,867.75 | 232,689,189.25 | 234,761,751.00 | 233,946,060.66 | 233,171,624.10 | 232,887,374.29 | 232,688,608.69 | 232,519,764.15 | 231,997,168.00 | 232,018,623.90 | 232,020,579.26 | 232,022,610.14 | 232,023,723.49 | 232,024,340.43 | 232,024,685.70 |
| 12/2017 | 193,690,346.50 | 241,381,936.25 | 248,638,909.75 | 245,126,638.75 | 247,774,394.00 | 246,116,372.79 | 245,261,230.30 | 244,449,336.89 | 244,151,338.90 | 243,942,959.68 | 243,765,948.71 | 243,218,076.38 | 243,240,570.02 | 243,242,619.96 | 243,244,749.07 | 243,245,916.26 | 243,246,563.04 | 243,246,925.01 |
| 12/2018 | 194,260,377.50 | 241,752,892.50 | 248,933,149.50 | 248,301,831.75 | 246,590,939.34 | 244,940,837.40 | 244,089,779.37 | 243,281,763.84 | 242,985,189.18 | 242,777,805.26 | 242,601,639.75 | 242,056,384.24 | 242,078,770.45 | 242,080,810.59 | 242,082,929.53 | 242,084,091.15 | 242,084,734.84 | 242,085,095.08 |
| 12/2019 | 204,718,780.00 | 258,748,269.50 | 269,575,517.75 | 269,061,534.14 | 267,207,599.63 | 265,419,538.07 | 264,497,325.87 | 263,621,754.81 | 263,300,384.52 | 263,075,661.90 | 262,884,767.77 | 262,293,925.24 | 262,318,183.08 | 262,320,393.79 | 262,322,689.89 | 262,323,948.63 | 262,324,646.14 | 262,325,036.50 |
| 12/2020 | 137,506,664.75 | 178,589,862.50 | 184,098,314.10 | 183,747,304.79 | 182,481,217.20 | 181,260,115.51 | 180,630,319.03 | 180,032,374.69 | 179,812,904.73 | 179,659,437.33 | 179,529,072.05 | 179,125,574.30 | 179,142,140.45 | 179,143,650.18 | 179,145,218.24 | 179,146,077.85 | 179,146,554.19 | 179,146,820.78 |
| 12/2021 | 189,587,392.75 | 241,911,485.00 | 249,373,037.90 | 248,897,573.16 | 247,182,575.87 | 245,528,514.90 | 244,675,414.96 | 243,865,460.78 | 243,568,174.57 | 243,360,293.08 | 243,183,704.90 | 242,637,141.18 | 242,659,581.10 | 242,661,626.13 | 242,663,750.16 | 242,664,914.57 | 242,665,559.80 | 242,665,920.90 |
Incurr_devel.diag()
[237139707.0, 238669835.25, 237407042.25, 243090398.25, 226246170.5, 218296573.25, 219193220.75, 239437836.75, 234761751.0, 247774394.0, 248301831.75, 269575517.75, 178589862.5, 189587392.75]
Incurr_devel.ibnr()
array([ 4.19704153e+03, 6.23557040e+03, 2.81593723e+04, -5.17585330e+05,
-6.45540990e+05, -8.08639647e+05, -1.07818060e+06, -1.96647836e+06,
-2.73706530e+06, -4.52746899e+06, -6.21673667e+06, -7.25048125e+06,
5.56958277e+05, 5.30785282e+07])
diag_payments = CumPaid_tr.diag()
Incurr_devel.reserve(case_reserves=None, payments=diag_payments)
array([ 4.19704153e+03, 1.43423207e+06, 8.66559872e+05, 2.92559392e+06,
-2.34751240e+05, 3.76722360e+06, 4.77169140e+06, 9.39240414e+06,
2.47604292e+07, 3.27852838e+07, 4.17953043e+07, 7.00235792e+07,
7.05096085e+07, 1.72212134e+08])
case_reserves = CaseRes_tr.diag()
Incurr_devel.reserve(case_reserves=case_reserves, payments=None)
array([ 4.19704153e+03, 1.43423207e+06, 8.66559872e+05, 2.92559392e+06,
-2.34751240e+05, 3.76722360e+06, 4.77169140e+06, 9.39240414e+06,
2.47604292e+07, 3.27852838e+07, 4.17953043e+07, 7.00235792e+07,
7.05096085e+07, 1.72212134e+08])
A continuación, se construye una proyección de IBNR y Reservas a partir del triángulo de pagos acumulados:
CumPaid_devel = CumPaid_tr.chainladder(dev_f=CumPaid_df)
CumPaid_devel.show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||
| 12/2008 | 59,769,792.25 | 165,450,290.25 | 199,870,725.25 | 217,710,186.75 | 226,508,362.50 | 231,561,596.00 | 234,583,184.50 | 235,492,526.50 | 235,842,953.50 | 236,679,451.75 | 236,830,634.25 | 237,088,328.75 | 237,137,708.50 | 237,139,707.00 |
| 12/2009 | 66,322,949.00 | 172,599,974.75 | 202,734,288.75 | 219,299,874.50 | 229,098,212.00 | 233,612,156.75 | 235,362,048.25 | 236,241,391.75 | 236,582,442.25 | 236,978,784.00 | 237,011,082.00 | 237,220,333.00 | 237,241,838.75 | 237,243,838.13 |
| 12/2010 | 65,872,992.50 | 171,545,542.00 | 204,518,830.25 | 219,677,340.75 | 228,315,913.00 | 230,619,957.75 | 232,128,895.25 | 233,760,436.00 | 234,838,481.50 | 235,400,644.50 | 235,481,167.25 | 236,568,641.75 | 236,603,996.97 | 236,605,990.97 |
| 12/2011 | 73,281,092.50 | 177,437,692.25 | 211,989,349.25 | 225,904,938.00 | 233,299,603.25 | 237,212,167.50 | 238,171,038.00 | 238,204,519.00 | 239,276,107.00 | 239,329,410.25 | 239,647,219.00 | 240,172,385.24 | 240,208,279.04 | 240,210,303.41 |
| 12/2012 | 71,133,350.75 | 170,462,076.75 | 202,128,321.50 | 215,426,247.75 | 220,361,960.00 | 223,714,366.75 | 224,830,359.25 | 225,441,690.25 | 225,710,275.00 | 225,835,380.75 | 225,973,924.99 | 226,469,127.38 | 226,502,973.23 | 226,504,882.10 |
| 12/2013 | 73,052,085.75 | 169,312,321.50 | 196,125,924.75 | 205,648,105.25 | 209,351,135.00 | 210,680,426.25 | 212,484,079.50 | 213,326,428.00 | 213,720,710.00 | 214,080,495.81 | 214,211,828.73 | 214,681,255.50 | 214,713,339.65 | 214,715,149.16 |
| 12/2014 | 80,029,486.25 | 167,411,221.25 | 191,426,151.00 | 202,659,814.00 | 207,440,765.00 | 209,990,095.00 | 211,954,827.00 | 213,343,348.75 | 213,884,085.24 | 214,244,146.09 | 214,375,579.40 | 214,845,365.01 | 214,877,473.69 | 214,879,284.59 |
| 12/2015 | 79,283,232.00 | 163,188,432.75 | 194,775,049.00 | 213,604,716.50 | 221,803,863.75 | 226,107,304.50 | 228,078,954.25 | 228,982,352.29 | 229,562,727.14 | 229,949,182.03 | 230,090,249.98 | 230,594,472.94 | 230,628,935.32 | 230,630,878.97 |
| 12/2016 | 76,831,315.75 | 149,990,867.25 | 176,481,879.00 | 194,354,543.25 | 203,591,533.25 | 207,264,256.50 | 208,884,139.07 | 209,711,508.36 | 210,243,039.65 | 210,596,971.01 | 210,726,166.88 | 211,187,955.12 | 211,219,517.19 | 211,221,297.26 |
| 12/2017 | 72,758,633.50 | 153,658,485.75 | 182,026,017.25 | 201,342,186.50 | 210,461,641.25 | 213,756,169.36 | 215,426,789.75 | 216,280,073.83 | 216,828,253.69 | 217,193,270.87 | 217,326,513.39 | 217,802,765.73 | 217,835,316.38 | 217,837,152.21 |
| 12/2018 | 75,059,369.00 | 153,899,163.25 | 185,599,785.00 | 200,289,790.75 | 207,352,765.59 | 210,598,627.93 | 212,244,570.42 | 213,085,250.04 | 213,625,332.36 | 213,984,957.61 | 214,116,231.91 | 214,585,449.19 | 214,617,519.02 | 214,619,327.73 |
| 12/2019 | 80,575,836.25 | 161,348,381.25 | 192,301,457.25 | 207,365,678.29 | 214,678,175.65 | 218,038,708.62 | 219,742,799.38 | 220,613,178.74 | 221,172,341.22 | 221,544,671.40 | 221,680,583.40 | 222,166,377.31 | 222,199,580.10 | 222,201,452.71 |
| 12/2020 | 52,497,772.25 | 108,637,212.25 | 128,628,290.39 | 138,704,579.07 | 143,595,826.64 | 145,843,649.49 | 146,983,496.71 | 147,565,683.71 | 147,939,701.23 | 148,188,748.72 | 148,279,658.73 | 148,604,600.83 | 148,626,809.81 | 148,628,062.38 |
| 12/2021 | 70,453,787.25 | 158,550,593.07 | 187,726,574.56 | 202,432,415.35 | 209,570,947.23 | 212,851,532.57 | 214,515,082.74 | 215,364,755.63 | 215,910,615.55 | 216,274,087.93 | 216,406,766.56 | 216,881,003.35 | 216,913,416.25 | 216,915,244.31 |
CumPaid_devel.diag()
[237139707.0, 237241838.75, 236568641.75, 239647219.0, 225835380.75, 213720710.0, 213343348.75, 228078954.25, 207264256.5, 210461641.25, 200289790.75, 192301457.25, 108637212.25, 70453787.25]
CumPaid_devel.ibnr(case_reserves=case_reserves)
array([ 0. , -1425997.12243265, -801051.27923012,
-2880094.83594602, 258711.60094556, -3581424.08501619,
-4313936.16355917, -8806957.78471813, -23540453.7358309 ,
-29937241.79195613, -33682504.01995134, -47374065.03833425,
-29961800.12235531, 27327851.55869642])
CumPaid_devel.reserve()
array([0.00000000e+00, 1.99937757e+03, 3.73492208e+04, 5.63084414e+05,
6.69501351e+05, 9.94439165e+05, 1.53593584e+06, 2.55192472e+06,
3.95704076e+06, 7.37551096e+06, 1.43295370e+07, 2.98999955e+07,
3.99908501e+07, 1.46461457e+08])
apriori_incurr=Incurr_devel.ultimate()
apriori_incurr[13] = apriori_incurr[13]*1.2
Incurr_devel_bf = Incurred_tr.bf(dev_f = incurred_df, a_priori_ult=apriori_incurr)
Incurr_devel_bf.show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||
| 12/2008 | 160,139,045.50 | 226,559,737.25 | 236,266,268.00 | 244,960,152.50 | 243,214,489.00 | 242,232,361.00 | 237,986,488.25 | 237,402,737.25 | 237,520,052.00 | 237,846,378.00 | 237,655,232.50 | 237,107,363.50 | 237,137,708.50 | 237,139,707.00 |
| 12/2009 | 170,668,596.00 | 229,474,322.00 | 241,053,886.50 | 247,883,002.50 | 246,231,580.00 | 242,918,107.25 | 241,458,780.50 | 240,670,060.75 | 240,441,831.00 | 238,746,816.00 | 238,458,078.25 | 238,656,180.00 | 238,669,835.25 | 238,671,846.70 |
| 12/2010 | 172,718,677.25 | 231,355,591.25 | 243,742,133.25 | 244,439,980.75 | 241,871,707.00 | 240,849,518.00 | 239,921,955.00 | 239,826,406.75 | 239,671,876.50 | 239,397,733.75 | 238,663,761.00 | 237,407,042.25 | 237,428,998.86 | 237,430,999.85 |
| 12/2011 | 183,979,363.75 | 241,276,966.00 | 249,143,599.25 | 249,556,895.00 | 247,601,653.25 | 244,683,960.50 | 243,566,232.00 | 243,056,439.50 | 241,679,172.00 | 242,572,099.00 | 243,090,398.25 | 242,544,034.57 | 242,566,466.27 | 242,568,510.56 |
| 12/2012 | 175,627,597.25 | 226,648,257.50 | 238,413,819.00 | 234,372,948.25 | 232,489,365.50 | 228,558,839.25 | 227,516,628.50 | 226,527,089.25 | 226,508,345.00 | 226,246,170.50 | 226,081,997.85 | 225,573,861.80 | 225,594,724.01 | 225,596,625.27 |
| 12/2013 | 177,484,462.75 | 223,476,284.50 | 223,127,831.50 | 221,309,161.50 | 219,625,833.00 | 217,998,572.75 | 219,304,239.00 | 218,348,907.00 | 218,296,573.25 | 218,110,257.36 | 217,951,988.43 | 217,462,125.17 | 217,482,237.17 | 217,484,070.06 |
| 12/2014 | 192,433,529.75 | 224,730,010.75 | 226,156,647.50 | 222,911,496.50 | 221,214,136.50 | 221,192,476.75 | 220,667,758.50 | 219,193,220.75 | 218,926,006.70 | 218,739,153.59 | 218,580,428.30 | 218,089,152.57 | 218,109,322.56 | 218,111,160.73 |
| 12/2015 | 195,675,030.25 | 248,325,743.75 | 250,155,328.50 | 243,339,946.50 | 240,425,484.25 | 237,945,648.50 | 239,437,836.75 | 238,645,206.62 | 238,354,279.03 | 238,150,843.89 | 237,978,032.75 | 237,443,159.43 | 237,465,119.38 | 237,467,120.68 |
| 12/2016 | 195,320,417.25 | 231,643,347.25 | 237,312,493.25 | 235,702,867.75 | 232,689,189.25 | 234,761,751.00 | 233,946,046.23 | 233,171,595.96 | 232,887,341.12 | 232,688,572.00 | 232,519,724.47 | 231,997,119.07 | 232,018,575.35 | 232,020,530.74 |
| 12/2017 | 193,690,346.50 | 241,381,936.25 | 248,638,909.75 | 245,126,638.75 | 247,774,394.00 | 246,116,343.44 | 245,261,185.82 | 244,449,278.05 | 244,151,274.77 | 243,942,891.87 | 243,765,877.77 | 243,217,995.74 | 243,240,489.78 | 243,242,539.75 |
| 12/2018 | 194,260,377.50 | 241,752,892.50 | 248,933,149.50 | 248,301,831.75 | 246,590,909.06 | 244,940,777.92 | 244,089,704.82 | 243,281,674.99 | 242,985,095.08 | 242,777,707.49 | 242,601,538.87 | 242,056,273.70 | 242,078,660.31 | 242,080,700.49 |
| 12/2019 | 204,718,780.00 | 258,748,269.50 | 269,575,517.75 | 269,061,525.05 | 267,207,557.72 | 265,419,464.52 | 264,497,235.99 | 263,621,649.43 | 263,300,273.45 | 263,075,546.86 | 262,884,649.36 | 262,293,796.36 | 262,318,054.64 | 262,320,265.39 |
| 12/2020 | 137,506,664.75 | 178,589,862.50 | 184,098,411.59 | 183,747,396.07 | 182,481,286.07 | 181,260,162.77 | 180,630,355.15 | 180,032,400.22 | 179,812,926.37 | 179,659,456.26 | 179,529,088.67 | 179,125,583.78 | 179,142,150.22 | 179,143,659.99 |
| 12/2021 | 189,587,392.75 | 252,377,414.73 | 261,331,436.68 | 260,760,868.89 | 258,702,835.72 | 256,717,927.43 | 255,694,189.37 | 254,722,227.17 | 254,365,477.39 | 254,116,015.19 | 253,904,105.63 | 253,248,217.55 | 253,275,145.93 | 253,277,600.02 |
Incurred_tr.bf(dev_f = incurred_df, a_priori_ult=apriori_incurr, tail_f = weibull_f).show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | Tail 1 | Tail 2 | Tail 3 | Tail 4 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||||||
| 12/2008 | 160,139,045.50 | 226,559,737.25 | 236,266,268.00 | 244,960,152.50 | 243,214,489.00 | 242,232,361.00 | 237,986,488.25 | 237,402,737.25 | 237,520,052.00 | 237,846,378.00 | 237,655,232.50 | 237,107,363.50 | 237,137,708.50 | 237,139,707.00 | 237,141,782.69 | 237,142,920.60 | 237,143,551.15 | 237,143,904.04 |
| 12/2009 | 170,668,596.00 | 229,474,322.00 | 241,053,886.50 | 247,883,002.50 | 246,231,580.00 | 242,918,107.25 | 241,458,780.50 | 240,670,060.75 | 240,441,831.00 | 238,746,816.00 | 238,458,078.25 | 238,656,180.00 | 238,669,835.25 | 238,671,846.66 | 238,673,935.77 | 238,675,081.03 | 238,675,715.65 | 238,676,070.82 |
| 12/2010 | 172,718,677.25 | 231,355,591.25 | 243,742,133.25 | 244,439,980.75 | 241,871,707.00 | 240,849,518.00 | 239,921,955.00 | 239,826,406.75 | 239,671,876.50 | 239,397,733.75 | 238,663,761.00 | 237,407,042.25 | 237,428,998.47 | 237,430,999.43 | 237,433,077.67 | 237,434,216.97 | 237,434,848.30 | 237,435,201.62 |
| 12/2011 | 183,979,363.75 | 241,276,966.00 | 249,143,599.25 | 249,556,895.00 | 247,601,653.25 | 244,683,960.50 | 243,566,232.00 | 243,056,439.50 | 241,679,172.00 | 242,572,099.00 | 243,090,398.25 | 242,544,044.24 | 242,566,475.55 | 242,568,519.80 | 242,570,643.01 | 242,571,806.97 | 242,572,451.95 | 242,572,812.92 |
| 12/2012 | 175,627,597.25 | 226,648,257.50 | 238,413,819.00 | 234,372,948.25 | 232,489,365.50 | 228,558,839.25 | 227,516,628.50 | 226,527,089.25 | 226,508,345.00 | 226,246,170.50 | 226,082,000.75 | 225,573,873.70 | 225,594,735.54 | 225,596,636.76 | 225,598,611.42 | 225,599,693.94 | 225,600,293.80 | 225,600,629.51 |
| 12/2013 | 177,484,462.75 | 223,476,284.50 | 223,127,831.50 | 221,309,161.50 | 219,625,833.00 | 217,998,572.75 | 219,304,239.00 | 218,348,907.00 | 218,296,573.25 | 218,110,260.66 | 217,951,994.53 | 217,462,139.94 | 217,482,251.59 | 217,484,084.44 | 217,485,988.09 | 217,487,031.68 | 217,487,609.97 | 217,487,933.60 |
| 12/2014 | 192,433,529.75 | 224,730,010.75 | 226,156,647.50 | 222,911,496.50 | 221,214,136.50 | 221,192,476.75 | 220,667,758.50 | 219,193,220.75 | 218,926,011.43 | 218,739,161.63 | 218,580,439.15 | 218,089,172.11 | 218,109,341.75 | 218,111,179.88 | 218,113,089.02 | 218,114,135.62 | 218,114,715.58 | 218,115,040.15 |
| 12/2015 | 195,675,030.25 | 248,325,743.75 | 250,155,328.50 | 243,339,946.50 | 240,425,484.25 | 237,945,648.50 | 239,437,836.75 | 238,645,220.64 | 238,354,298.20 | 238,150,866.67 | 237,978,058.58 | 237,443,194.73 | 237,465,154.29 | 237,467,155.55 | 237,469,234.11 | 237,470,373.59 | 237,471,005.02 | 237,471,358.39 |
| 12/2016 | 195,320,417.25 | 231,643,347.25 | 237,312,493.25 | 235,702,867.75 | 232,689,189.25 | 234,761,751.00 | 233,946,060.66 | 233,171,624.10 | 232,887,374.29 | 232,688,608.69 | 232,519,764.15 | 231,997,168.00 | 232,018,623.90 | 232,020,579.26 | 232,022,610.14 | 232,023,723.49 | 232,024,340.43 | 232,024,685.70 |
| 12/2017 | 193,690,346.50 | 241,381,936.25 | 248,638,909.75 | 245,126,638.75 | 247,774,394.00 | 246,116,372.79 | 245,261,230.30 | 244,449,336.89 | 244,151,338.90 | 243,942,959.68 | 243,765,948.71 | 243,218,076.38 | 243,240,570.02 | 243,242,619.96 | 243,244,749.07 | 243,245,916.26 | 243,246,563.04 | 243,246,925.01 |
| 12/2018 | 194,260,377.50 | 241,752,892.50 | 248,933,149.50 | 248,301,831.75 | 246,590,939.34 | 244,940,837.40 | 244,089,779.37 | 243,281,763.84 | 242,985,189.18 | 242,777,805.26 | 242,601,639.75 | 242,056,384.24 | 242,078,770.45 | 242,080,810.59 | 242,082,929.53 | 242,084,091.15 | 242,084,734.84 | 242,085,095.08 |
| 12/2019 | 204,718,780.00 | 258,748,269.50 | 269,575,517.75 | 269,061,534.14 | 267,207,599.63 | 265,419,538.07 | 264,497,325.87 | 263,621,754.81 | 263,300,384.52 | 263,075,661.90 | 262,884,767.77 | 262,293,925.24 | 262,318,183.08 | 262,320,393.79 | 262,322,689.89 | 262,323,948.63 | 262,324,646.14 | 262,325,036.50 |
| 12/2020 | 137,506,664.75 | 178,589,862.50 | 184,098,314.10 | 183,747,304.79 | 182,481,217.20 | 181,260,115.51 | 180,630,319.03 | 180,032,374.69 | 179,812,904.73 | 179,659,437.33 | 179,529,072.05 | 179,125,574.30 | 179,142,140.45 | 179,143,650.18 | 179,145,218.24 | 179,146,077.85 | 179,146,554.19 | 179,146,820.78 |
| 12/2021 | 189,587,392.75 | 252,376,303.45 | 261,330,166.93 | 260,759,609.24 | 258,701,612.50 | 256,716,739.33 | 255,693,019.40 | 254,721,074.39 | 254,364,330.93 | 254,114,873.14 | 253,902,967.33 | 253,247,090.86 | 253,274,018.77 | 253,276,472.81 | 253,279,021.64 | 253,280,418.93 | 253,281,193.21 | 253,281,626.54 |
Incurr_devel_bf.diag()
[237139707.0, 238669835.25, 237407042.25, 243090398.25, 226246170.5, 218296573.25, 219193220.75, 239437836.75, 234761751.0, 247774394.0, 248301831.75, 269575517.75, 178589862.5, 189587392.75]
Incurr_devel_bf.ibnr()
array([ 0.00000000e+00, 2.01144774e+03, 2.39575993e+04, -5.21887690e+05,
-6.49545231e+05, -8.12503191e+05, -1.08206002e+06, -1.97071607e+06,
-2.74122026e+06, -4.53185425e+06, -6.22113126e+06, -7.25525236e+06,
5.53797486e+05, 6.36902073e+07])
Incurr_devel_bf.reserve(case_reserves=case_reserves, payments=None)
array([ 0.00000000e+00, 1.43000795e+06, 8.62358099e+05, 2.92129156e+06,
-2.38755481e+05, 3.76336006e+06, 4.76781198e+06, 9.38816643e+06,
2.47562742e+07, 3.27808985e+07, 4.17909097e+07, 7.00188081e+07,
7.05064477e+07, 1.82823813e+08])
ultimate_cl=Incurr_devel.ultimate()
premiums = [x * 0.75 for x in ultimate_cl]
premiums # 75% LR is assumed over Ultimate in CL in order to develope the example.
[177857928.0311497, 179007053.1153035, 178076401.21669278, 181929609.69031346, 169200472.13226306, 163115950.2022591, 163586280.1098099, 178103518.79322892, 174018514.27309698, 182435193.75719917, 181563821.3112195, 196743777.37300885, 134360115.58275396, 181999440.67859352]
Incurr_devel_cc = Incurred_tr.cape_cod(dev_f = incurred_df, premiums=premiums)
Incurr_devel_bf.show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||
| 12/2008 | 160,139,045.50 | 226,559,737.25 | 236,266,268.00 | 244,960,152.50 | 243,214,489.00 | 242,232,361.00 | 237,986,488.25 | 237,402,737.25 | 237,520,052.00 | 237,846,378.00 | 237,655,232.50 | 237,107,363.50 | 237,137,708.50 | 237,139,707.00 |
| 12/2009 | 170,668,596.00 | 229,474,322.00 | 241,053,886.50 | 247,883,002.50 | 246,231,580.00 | 242,918,107.25 | 241,458,780.50 | 240,670,060.75 | 240,441,831.00 | 238,746,816.00 | 238,458,078.25 | 238,656,180.00 | 238,669,835.25 | 238,671,846.70 |
| 12/2010 | 172,718,677.25 | 231,355,591.25 | 243,742,133.25 | 244,439,980.75 | 241,871,707.00 | 240,849,518.00 | 239,921,955.00 | 239,826,406.75 | 239,671,876.50 | 239,397,733.75 | 238,663,761.00 | 237,407,042.25 | 237,428,998.86 | 237,430,999.85 |
| 12/2011 | 183,979,363.75 | 241,276,966.00 | 249,143,599.25 | 249,556,895.00 | 247,601,653.25 | 244,683,960.50 | 243,566,232.00 | 243,056,439.50 | 241,679,172.00 | 242,572,099.00 | 243,090,398.25 | 242,544,034.57 | 242,566,466.27 | 242,568,510.56 |
| 12/2012 | 175,627,597.25 | 226,648,257.50 | 238,413,819.00 | 234,372,948.25 | 232,489,365.50 | 228,558,839.25 | 227,516,628.50 | 226,527,089.25 | 226,508,345.00 | 226,246,170.50 | 226,081,997.85 | 225,573,861.80 | 225,594,724.01 | 225,596,625.27 |
| 12/2013 | 177,484,462.75 | 223,476,284.50 | 223,127,831.50 | 221,309,161.50 | 219,625,833.00 | 217,998,572.75 | 219,304,239.00 | 218,348,907.00 | 218,296,573.25 | 218,110,257.36 | 217,951,988.43 | 217,462,125.17 | 217,482,237.17 | 217,484,070.06 |
| 12/2014 | 192,433,529.75 | 224,730,010.75 | 226,156,647.50 | 222,911,496.50 | 221,214,136.50 | 221,192,476.75 | 220,667,758.50 | 219,193,220.75 | 218,926,006.70 | 218,739,153.59 | 218,580,428.30 | 218,089,152.57 | 218,109,322.56 | 218,111,160.73 |
| 12/2015 | 195,675,030.25 | 248,325,743.75 | 250,155,328.50 | 243,339,946.50 | 240,425,484.25 | 237,945,648.50 | 239,437,836.75 | 238,645,206.62 | 238,354,279.03 | 238,150,843.89 | 237,978,032.75 | 237,443,159.43 | 237,465,119.38 | 237,467,120.68 |
| 12/2016 | 195,320,417.25 | 231,643,347.25 | 237,312,493.25 | 235,702,867.75 | 232,689,189.25 | 234,761,751.00 | 233,946,046.23 | 233,171,595.96 | 232,887,341.12 | 232,688,572.00 | 232,519,724.47 | 231,997,119.07 | 232,018,575.35 | 232,020,530.74 |
| 12/2017 | 193,690,346.50 | 241,381,936.25 | 248,638,909.75 | 245,126,638.75 | 247,774,394.00 | 246,116,343.44 | 245,261,185.82 | 244,449,278.05 | 244,151,274.77 | 243,942,891.87 | 243,765,877.77 | 243,217,995.74 | 243,240,489.78 | 243,242,539.75 |
| 12/2018 | 194,260,377.50 | 241,752,892.50 | 248,933,149.50 | 248,301,831.75 | 246,590,909.06 | 244,940,777.92 | 244,089,704.82 | 243,281,674.99 | 242,985,095.08 | 242,777,707.49 | 242,601,538.87 | 242,056,273.70 | 242,078,660.31 | 242,080,700.49 |
| 12/2019 | 204,718,780.00 | 258,748,269.50 | 269,575,517.75 | 269,061,525.05 | 267,207,557.72 | 265,419,464.52 | 264,497,235.99 | 263,621,649.43 | 263,300,273.45 | 263,075,546.86 | 262,884,649.36 | 262,293,796.36 | 262,318,054.64 | 262,320,265.39 |
| 12/2020 | 137,506,664.75 | 178,589,862.50 | 184,098,411.59 | 183,747,396.07 | 182,481,286.07 | 181,260,162.77 | 180,630,355.15 | 180,032,400.22 | 179,812,926.37 | 179,659,456.26 | 179,529,088.67 | 179,125,583.78 | 179,142,150.22 | 179,143,659.99 |
| 12/2021 | 189,587,392.75 | 252,377,414.73 | 261,331,436.68 | 260,760,868.89 | 258,702,835.72 | 256,717,927.43 | 255,694,189.37 | 254,722,227.17 | 254,365,477.39 | 254,116,015.19 | 253,904,105.63 | 253,248,217.55 | 253,275,145.93 | 253,277,600.02 |
Incurr_devel_cc_tail = Incurred_tr.cape_cod(dev_f = incurred_df, premiums = premiums, tail_f = weibull_f)
Incurr_devel_cc_tail.show()
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | Tail 1 | Tail 2 | Tail 3 | Tail 4 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AccidentYear | ||||||||||||||||||
| 12/2008 | 160,139,045.50 | 226,559,737.25 | 236,266,268.00 | 244,960,152.50 | 243,214,489.00 | 242,232,361.00 | 237,986,488.25 | 237,402,737.25 | 237,520,052.00 | 237,846,378.00 | 237,655,232.50 | 237,107,363.50 | 237,137,708.50 | 237,139,707.00 | 237,141,782.69 | 237,142,920.60 | 237,143,551.15 | 237,143,904.04 |
| 12/2009 | 170,668,596.00 | 229,474,322.00 | 241,053,886.50 | 247,883,002.50 | 246,231,580.00 | 242,918,107.25 | 241,458,780.50 | 240,670,060.75 | 240,441,831.00 | 238,746,816.00 | 238,458,078.25 | 238,656,180.00 | 238,669,835.25 | 238,671,846.66 | 238,673,935.77 | 238,675,081.03 | 238,675,715.65 | 238,676,070.82 |
| 12/2010 | 172,718,677.25 | 231,355,591.25 | 243,742,133.25 | 244,439,980.75 | 241,871,707.00 | 240,849,518.00 | 239,921,955.00 | 239,826,406.75 | 239,671,876.50 | 239,397,733.75 | 238,663,761.00 | 237,407,042.25 | 237,428,998.47 | 237,430,999.43 | 237,433,077.67 | 237,434,216.97 | 237,434,848.30 | 237,435,201.62 |
| 12/2011 | 183,979,363.75 | 241,276,966.00 | 249,143,599.25 | 249,556,895.00 | 247,601,653.25 | 244,683,960.50 | 243,566,232.00 | 243,056,439.50 | 241,679,172.00 | 242,572,099.00 | 243,090,398.25 | 242,544,044.24 | 242,566,475.55 | 242,568,519.80 | 242,570,643.01 | 242,571,806.97 | 242,572,451.95 | 242,572,812.92 |
| 12/2012 | 175,627,597.25 | 226,648,257.50 | 238,413,819.00 | 234,372,948.25 | 232,489,365.50 | 228,558,839.25 | 227,516,628.50 | 226,527,089.25 | 226,508,345.00 | 226,246,170.50 | 226,082,000.75 | 225,573,873.70 | 225,594,735.54 | 225,596,636.76 | 225,598,611.42 | 225,599,693.94 | 225,600,293.80 | 225,600,629.51 |
| 12/2013 | 177,484,462.75 | 223,476,284.50 | 223,127,831.50 | 221,309,161.50 | 219,625,833.00 | 217,998,572.75 | 219,304,239.00 | 218,348,907.00 | 218,296,573.25 | 218,110,260.66 | 217,951,994.53 | 217,462,139.94 | 217,482,251.59 | 217,484,084.44 | 217,485,988.09 | 217,487,031.68 | 217,487,609.97 | 217,487,933.60 |
| 12/2014 | 192,433,529.75 | 224,730,010.75 | 226,156,647.50 | 222,911,496.50 | 221,214,136.50 | 221,192,476.75 | 220,667,758.50 | 219,193,220.75 | 218,926,011.43 | 218,739,161.63 | 218,580,439.15 | 218,089,172.11 | 218,109,341.75 | 218,111,179.88 | 218,113,089.02 | 218,114,135.62 | 218,114,715.58 | 218,115,040.15 |
| 12/2015 | 195,675,030.25 | 248,325,743.75 | 250,155,328.50 | 243,339,946.50 | 240,425,484.25 | 237,945,648.50 | 239,437,836.75 | 238,645,220.64 | 238,354,298.20 | 238,150,866.67 | 237,978,058.58 | 237,443,194.73 | 237,465,154.29 | 237,467,155.55 | 237,469,234.11 | 237,470,373.59 | 237,471,005.02 | 237,471,358.39 |
| 12/2016 | 195,320,417.25 | 231,643,347.25 | 237,312,493.25 | 235,702,867.75 | 232,689,189.25 | 234,761,751.00 | 233,946,060.66 | 233,171,624.10 | 232,887,374.29 | 232,688,608.69 | 232,519,764.15 | 231,997,168.00 | 232,018,623.90 | 232,020,579.26 | 232,022,610.14 | 232,023,723.49 | 232,024,340.43 | 232,024,685.70 |
| 12/2017 | 193,690,346.50 | 241,381,936.25 | 248,638,909.75 | 245,126,638.75 | 247,774,394.00 | 246,116,372.79 | 245,261,230.30 | 244,449,336.89 | 244,151,338.90 | 243,942,959.68 | 243,765,948.71 | 243,218,076.38 | 243,240,570.02 | 243,242,619.96 | 243,244,749.07 | 243,245,916.26 | 243,246,563.04 | 243,246,925.01 |
| 12/2018 | 194,260,377.50 | 241,752,892.50 | 248,933,149.50 | 248,301,831.75 | 246,590,939.34 | 244,940,837.40 | 244,089,779.37 | 243,281,763.84 | 242,985,189.18 | 242,777,805.26 | 242,601,639.75 | 242,056,384.24 | 242,078,770.45 | 242,080,810.59 | 242,082,929.53 | 242,084,091.15 | 242,084,734.84 | 242,085,095.08 |
| 12/2019 | 204,718,780.00 | 258,748,269.50 | 269,575,517.75 | 269,061,534.14 | 267,207,599.63 | 265,419,538.07 | 264,497,325.87 | 263,621,754.81 | 263,300,384.52 | 263,075,661.90 | 262,884,767.77 | 262,293,925.24 | 262,318,183.08 | 262,320,393.79 | 262,322,689.89 | 262,323,948.63 | 262,324,646.14 | 262,325,036.50 |
| 12/2020 | 137,506,664.75 | 178,589,862.50 | 184,098,314.10 | 183,747,304.79 | 182,481,217.20 | 181,260,115.51 | 180,630,319.03 | 180,032,374.69 | 179,812,904.73 | 179,659,437.33 | 179,529,072.05 | 179,125,574.30 | 179,142,140.45 | 179,143,650.18 | 179,145,218.24 | 179,146,077.85 | 179,146,554.19 | 179,146,820.78 |
| 12/2021 | 189,587,392.75 | 241,911,485.00 | 249,373,037.90 | 248,897,573.16 | 247,182,575.87 | 245,528,514.90 | 244,675,414.96 | 243,865,460.78 | 243,568,174.57 | 243,360,293.08 | 243,183,704.90 | 242,637,141.18 | 242,659,581.10 | 242,661,626.13 | 242,663,750.16 | 242,664,914.57 | 242,665,559.80 | 242,665,920.90 |
Incurr_devel_cc_tail.diag()
[237139707.0, 238669835.25, 237407042.25, 243090398.25, 226246170.5, 218296573.25, 219193220.75, 239437836.75, 234761751.0, 247774394.0, 248301831.75, 269575517.75, 178589862.5, 189587392.75]
Incurr_devel_cc_tail.ibnr()
array([ 4.19704153e+03, 6.23557040e+03, 2.81593723e+04, -5.17585330e+05,
-6.45540990e+05, -8.08639647e+05, -1.07818060e+06, -1.96647836e+06,
-2.73706530e+06, -4.52746899e+06, -6.21673667e+06, -7.25048125e+06,
5.56958277e+05, 5.30785282e+07])
Incurr_devel_cc_tail.reserve(case_reserves=case_reserves, payments=None)
array([ 4.19704153e+03, 1.43423207e+06, 8.66559872e+05, 2.92559392e+06,
-2.34751240e+05, 3.76722360e+06, 4.77169140e+06, 9.39240414e+06,
2.47604292e+07, 3.27852838e+07, 4.17953043e+07, 7.00235792e+07,
7.05096085e+07, 1.72212134e+08])
cf.cash_flows(Incurr_devel_bf)
[3052598998.7477627, 2816276699.126035, 2572444575.4023347, 2323727804.009294, 2093454195.4877944, 1873143847.4960198, 1652915931.0330164, 1414226877.2332761, 1181260100.279608, 937428444.5308765, 694710633.1620016, 432418805.9165312, 253277600.01734892]